The problem of analysis strategies for adaptive designs with multiple endpoints is considered. We first provide a review of the commonly used methods for addressing the issue of multiplicity in classical designs, followed by the gatekeeper procedure and the fractal gatekeeper procedure. The latter will be applied to address the issue of multiplicity in adaptive trials with multiple endpoints based on the invariance property of the test statistic employed. Practical examples are presented to illustrate the proposed fractal gatekeeper method when analyzing data obtained from an adaptive trial with multiple endpoints.